Dividing and factorising polynomial expressionsSynthetic division

A polynomial is an algebraic expression involving many terms and can be factorised using long division or synthetic division.

Part ofMathsAlgebraic and trigonometric skills

Synthetic division

Watch this video to learn about synthetic division of polynomials.

Synthetic division is another, easier, way of carrying out division of polynomials.

Look at how it would work for the example above before moving on to an explanation of the process.

\(({x^2} + 7x + 3) \div (x - 1)\)

Using synthetic division to divide an algebraic expression

\({x^2} + 7x + 3 = (x - 1)(x + 8) + 11\)

where \((x - 1)\) is the divisor, \((x + 8)\) is the quotient and \(11\) is the remainder.